- #1
Nikitin
- 735
- 27
Distributions: sample mean and variance, and variance of sample means?
Hi. Say you have a population, and from there you can draw a stochastic variable ##X## with a specified distribution. So you take out a few sizeable samples from the population, and calculate the mean and variance of ##X## for each sample.
A few easy questions:
1) What distribution will ##\bar{X}## have? I assume it will have the same distribution as ##X##? Makes intuitive sense, but can somebody explain it to me anyway?
2) What distribution will ##Var(X)## have?
3) What will the distribution of ##Var(\bar{X})## be? From the central limit theorem, I know that ##E(\bar{X})## has a normal distribution. But what about the variance?
thanks for help :)
Hi. Say you have a population, and from there you can draw a stochastic variable ##X## with a specified distribution. So you take out a few sizeable samples from the population, and calculate the mean and variance of ##X## for each sample.
A few easy questions:
1) What distribution will ##\bar{X}## have? I assume it will have the same distribution as ##X##? Makes intuitive sense, but can somebody explain it to me anyway?
2) What distribution will ##Var(X)## have?
3) What will the distribution of ##Var(\bar{X})## be? From the central limit theorem, I know that ##E(\bar{X})## has a normal distribution. But what about the variance?
thanks for help :)
Last edited: